Budarina, Natalia and Dickinson, Detta and Bernik, Vasili
(2010)
Simultaneous Diophantine approximation in the real, complex and p–adic fields.
Mathematical Proceedings of the Cambridge Philosophical Society, 149 (2).
pp. 193216.
ISSN 14698064
Abstract
In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ then the set of points (x, z, w) ∈ ℝ × ℂ × ℚp which simultaneously satisfy the inequalities P(x) ≤ H−v1 Ψλ1(H), P(z) ≤ H−v2 Ψλ2(H) and P(w)p ≤ H−v3 Ψλ3(H) with v1 + 2v2 + v3 = n − 3 and λ1 + 2λ2 + λ3 = 1 for infinitely many integer polynomials P has measure zero.
Item Type: 
Article

Additional Information: 
Cite as: BUDARINA, N., DICKINSON, D., & BERNIK, V. (2010). Simultaneous Diophantine approximation in the real, complex and p–adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 149(2), 193216. doi:10.1017/S0305004110000162 
Keywords: 
Simultaneous Diophantine approximation; real, complex and p–adic fields; 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
10110 
Identification Number: 
https://doi.org/10.1017/S0305004110000162 
Depositing User: 
Dr. Detta Dickinson

Date Deposited: 
16 Oct 2018 16:38 
Journal or Publication Title: 
Mathematical Proceedings of the Cambridge Philosophical Society 
Publisher: 
Cambridge University Press 
Refereed: 
Yes 
URI: 

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